Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://hea-www.harvard.edu/QEDT/Papers/lbqs.ps Äàòà èçìåíåíèÿ: Sat Aug 12 01:04:07 1995 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 23:01:15 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: guide 8.0

THE SOFT X­RAY PROPERTIES
OF A LARGE OPTICAL QSO SAMPLE:
ROSAT OBSERVATIONS OF THE LARGE BRIGHT QUASAR
SURVEY
Paul J. Green 1;2 , Norbert Schartel 3 , Scott F. Anderson 4 , Paul C. Hewett 5 , Craig B. Foltz 6
Wolfgang Brinkmann 3 , Henner Fink 3 , Joachim Tr¨umper 3 , and Bruce Margon 4
Received October 20, 1994; accepted March 14, 1995
1 Harvard­Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138
2 Hubble Fellow
3 Max Planck Institut f¨ur extraterrestrische Physik, Giessenbachstr. 1, D­85740 Garching
bei M¨unchen, Germany
4 Astronomy Department, University of Washington, Seattle, WA 98195
5 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge
CB3 0HA, UK
6 Multiple Mirror Telescope Observatory, University of Arizona, Tucson, AZ 85721

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ABSTRACT
Of the more than 1000 QSOs in the Large Bright Quasar Survey (LBQS),
we study the X­ray properties of 908 that were covered by the ROSAT All­Sky
Survey (RASS). These data constitute among the largest, most homogeneous
X­ray surveys of QSOs to date, and as such are well­suited to the study of
the multiwavelength properties of QSOs. Due to the ú 600 s RASS exposure
times, only 10% of the QSOs are detected in X­rays. However, by stacking
X­ray counts, we obtain effectively much more sensitive observations for an
average QSO in bins of redshift or luminosity, and for several classes of QSOs.
We confirm a correlation of ff ox with luminosity for the overall sample. For
higher redshifts and optical luminosities, radio­loud QSOs appear to become
progressively more luminous in X­rays than radio­quiet QSOs. The X­ray
properties of a subsample of 36 BAL QSOs suggest that they are strongly
absorbed or underluminous in the X­rays, while a subsample of 22 FeII­strong
QSOs is anomalously X­ray bright.
Subject headings: galaxies: active --- quasars: general --- X­rays: galaxies

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1. INTRODUCTION
The ROSAT X­ray satellite (Tr¨umper 1983) was launched in 1990 June, and soon after
began the first all­sky soft X­ray survey. The ROSAT All­Sky Survey (RASS) benefits
from the low intrinsic background of the Position Sensitive Proportional Counter (PSPC,
Pfeffermann et al. 1987), and the large collecting area and field­of­view of the ROSAT
telescope (Aschenbach 1988). The RASS provides X­ray information (detections or upper
limits) for several thousand previously cataloged quasi­stellar objects (hereafter, QSOs).
Such data are relevant to X­ray luminosity functions, the X­ray evolution of QSOs, and
hence the contribution of QSOs to the diffuse X­ray background (XRB). The relationship
between the X­ray and other wavelength regimes elucidates the nature, origin, and energetics
of continuum and emission line processes in QSOs. Detailed multiwavelength studies of
individual objects can be very revealing, but large samples permit sound statistical tests
that place more anecdotal results in context.
X­ray observations of samples selected in other wavebands (e.g., optical or radio)
provide information complementary to X­ray­selected samples (e.g., Bade et al. 1992,
Franceschini et al. 1994). For instance, the Shanks et al. (1991) optical followup of X­ray
sources in a 30 ksec ROSAT PSPC image revealed about 10% more QSOs than were
cataloged in a UV excess (UVX) survey of the same field to B Ÿ 21 (Boyle et al. 1990). On
the other hand, 4 of 16 UVX QSOs remained undetected by ROSAT. This illustrates that
all QSO samples suffer from some incompleteness and/or selection effects. Nevertheless,
combinations of automated selection techniques have recently led to optically­selected QSO
samples that are remarkably well­defined and quantifiable. Extensive catalogs of faint QSOs
(e.g. Warren, Hewett & Osmer 1994, Boyle et al. 1990, Koo, Kron, & Cudworth 1986)
have proved useful for studies of space densities and evolution, but are too faint for detailed
optical spectra or detection in wavebands other than the optical using reasonable exposure
times. The Bright QSO Survey of Schmidt & Green (1986) is a well­studied exception, but
one that is dominated by low­redshift QSOs. Furthermore, that sample is too small (ú 100
objects) to provide statistically valuable samples of specific classes of QSOs (e.g., broad
absorption line, radio­loud, or strong FeII QSOs).
To take advantage of the unique attributes of the RASS (e.g., over previous Einstein
observations), a homogeneous optical QSO sample ideally would be (1) large, with a wide
range of redshifts and luminosities; (2) selected from extensive areal sky coverage; (3)
apparently bright, so that a significant fraction will be detected or have sensitive upper
limits in the RASS; (4) uniformly­selected, with quantifiable selection criteria so that
selection biases are well understood; (5) complemented by homogeneous, high quality data
in other wavebands. Such a sample, the Large Bright Quasar Survey (LBQS, described in

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the next section) has been been partly characterized in X­rays by Margon et al. (1992)
using 146 LBQS QSOs observed by Einstein. The RASS data now enable us to study the
X­ray properties of nearly the entire LBQS sample, permitting further division into specific
subsamples. Section 3. outlines the ROSAT data and our X­ray analysis. We discuss the
optical­to­X­ray properties of the full sample in x 4. Three subsamples ­ radio­loud, broad
absorption line, and FeII strong QSOs, are compared to appropriate control samples in the
following three sections, followed by our conclusions in x 8. The statistical techniques we
employ are detailed in an appendix.
2. THE LBQS QSO SAMPLE
The Large Bright Quasar Survey (Hewett, Foltz & Chaffee 1994, Morris et al. 1991,
Chaffee et al. 1991, Hewett et al. 1991, Foltz et al. 1989, Foltz et al. 1987) is a large,
uniformly­selected sample of QSOs with a wide range of redshifts. LBQS QSO candidates
were selected using the Automatic Plate Measuring Machine (APM; see Irwin & Trimble
1984) to scan UK Schmidt direct photographic and objective prism plates (see Hewett
et al. 1985 for a description of the objective­prism plate scanning procedures and the
basic selection algorithms). A combination of quantifiable selection techniques were
used, including color­selection, selection of objects with strong emission lines, selection
of objects having redshifted absorption features or continuum breaks. As described in
the series of LBQS papers, the technique appears to be highly efficient at finding QSOs
with 0:2 ! z ! 3:3, a significantly broader range than past work. Follow­up (6 \Gamma 10 š A
resolution) optical spectra with S/Nú10 in the continuum at 4500 š A were obtained at the
MMT and 2.5m duPont telescopes.
The entire LBQS optical sample here consists of 1056 QSOs over more than 450 deg 2
of the sky, with 16:0 Ÿ B J Ÿ 18:9. All 18 fields included in the LBQS were surveyed to
B J = 18:41, although the deepest field extended to B J = 18:85. Most of the LBQS QSOs
are sufficiently bright that even the RASS non­detections contribute useful information on
the average X­ray properties of QSOs. Redshifts range from 0.2 to 3.4, with a mean of 1.3.
The low redshift cutoff was arbitrarily imposed on the LBQS to avoid spatially extended
objects that otherwise meet the selection criteria.
The large sample size of the LBQS offers several advantages. First, one can average
QSOs in relatively fine bins of optical luminosity or redshift, while maintaining enough
objects per bin to allow a meaningful determination of average QSO X­ray properties as
a function of redshift and optical luminosity. Since Galactic hydrogen column density NH
(together with X­ray spectral slope) determines X­ray counts­to­flux conversion factors, the

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ability to also bin in NH provides a valuable check on the influence of NH on our results.
Second, relatively rare types of QSOs are present in large numbers; for example, there are
over 30 broad absorption line (hereafter, BAL) QSOs in the LBQS.
For ease of comparison with other work, we convert optical magnitudes originally in
the B J band to the B band using B = B J + 0:28(B \Gamma V ) (Blair & Gilmore 1982), assuming
B \Gamma V = 0:3. We apply a correction for extinction using the results of Burstein & Heiles
(1978, 1982) and assuming AB = 4:0 E(B \Gamma V ). The fit of Fisher and Tully (1981) is used
where Burstein & Heiles' data are not reliable. Our extinction­corrected apparent blue
magnitudes thus have a mean of 18.2. We make no correction to the optical magnitudes
for emission lines. Such a correction will vary with redshift and between QSOs, but in the
mean would represent an increase of ú 0:2 to the B J magnitudes of QSOs with z ! 3.
Composite QSO spectra (Francis et al. 1991, Cristiani & Vio 1990) show optical
slopes between --0.3 and --0.7, with quoted errors of \Sigma0:2). We calculate the K­corrections
and conversions between different rest­frame wavelengths by assuming an intrinsic optical
spectrum f š / š \Gamma0:5 . Throughout this paper, luminosities are calculated assuming H 0 = 50
km s \Gamma1 Mpc \Gamma1 and q 0 = 0:5, with specific optical normalization from Marshall et al. (1984).
Even though the LBQS QSOs are apparently bright, objects in substantial numbers
are represented over a very wide range of absolute magnitudes, \Gamma22 ! MB ! \Gamma28:6. This
corresponds to optical (rest frame 2500 š A) luminosities from 29.4 to 32.0 in the logarithm,
a factor of about 400 in intrinsic optical power. The mean log l opt of the LBQS/RASS
sample is 30:9 \Sigma 0:5.
3. ROSAT X­RAY OBSERVATIONS AND DETECTION CRITERIA
The Position Sensitive Proportional Counter (PSPC) of the ROSAT X­ray satellite
performed an All­Sky Survey (hereafter RASS) in the soft X­ray band (0.1 -- 2.4keV)
between 1990 August and 1991 February. A typical limiting flux for source detection (ú 4oe)
is a few times 10 \Gamma13 erg cm \Gamma2 s \Gamma1 , depending on the actual NH value and the spectral slope
of the source.
We removed from consideration all LBQS QSOs within 1:72 ffi of the approximate X­ray
center of the Virgo Cluster, since this region is contaminated by strong extended cluster
emission. To insure that background estimation would be of sufficient quality, we adopted
300 s as a minimum ROSAT exposure time for inclusion in our sample, a criterion that
excludes 20 QSOs. Exposure times thus range from 300 to 690 s, with a mean of 560 s.
Of the 1056 LBQS QSOs here, two lack reliable B J magnitudes due to image overlap. We

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also excluded data from regions with uncertain aspect solutions; this excludes 82 QSOs
mostly in LBQS fields 0300+0000 and 1240+0000. Our photon positional data are thus
subject only to random errors, of order 5 to 7 00 . Exclusion of the Virgo region and QSOs
near other extended or unrelated X­ray bright sources removes a further 44 QSOs from the
sample. This leaves 908 QSOs comprising the LBQS/RASS sample. Basic properties of the
LBQS/RASS sample are illustrated in Figure 1.
The high galactic latitude of the LBQS fields, together with the typical RASS
exposure times result in a RASS source density sufficiently low that simple X­ray aperture
photometry is adequate. To measure the mean background, an annulus from 600 to 1200 00
provides adequate background flux, but completely avoids the wings of bright source point
spread functions. Any source found by the ROSAT Extended Scientific Analysis System
(EXSAS, Zimmerman et al. 1993) to have maximum likelihood 6 or greater (ML=\Gammaln p)
we excise from this background region. We determined the optimal source aperture for high
signal­to­noise ratio (SNR) as follows: using a preliminary list of LBQS/RASS ML?10
detections, we calculated the average SNR for 24 different source apertures with radii from
50 to 400 00 . Since a broad maximum appears centered at 180 00 , we have adopted this as the
optimal aperture radius for faint sources in the RASS.
Next, by cross­correlating ML=6 EXSAS detections with the LBQS positions, we
empirically determined the maximum optimal X­ray/optical distance for accepting a
positional coincidence. The distance at which the histogram of total source coincidences
reaches a minimum before rising again (due to an increasing number of unrelated
coincidences) is 50 00 , which corresponds well to the PSPC positional errors in the RASS.
We therefore require the separation between the X­ray and optical positions to be ! 50 00 .
To avoid any possibility of contamination, we also eliminated (22) LBQS QSOs that had a
ML=6 EXSAS detection in the source aperture between 50 and 180 00 .
The source count rate is R src = (C tot \GammaC s
bkg
)
T
, where C tot is the total number of counts
in the source aperture, and C s
bkg is the number of counts in the background annulus,
normalized by the ratio of source area to background area A s =A b . The error in count rate
for the source may be expressed in terms of the area­normalized count rates, R src and R s
bkg
and the exposure time T , as
oe src =
s
R src + (1 +A s =A b )R s
bkg
T
In determining the optimal threshold for source detection, two types of contamination
of the ROSAT LBQS observations were considered ­ the chance coincidence of unrelated
X­ray sources, and random background fluctuations. Both increase the contamination of

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ROSAT­detected objects as the detection threshold is lowered. The most reliable way to
estimate the contamination from both causes is to run the detection algorithm both at the
actual (optical) LBQS positions and for a comparably sized control sample. We generated
a control sample of 710 positions at least 6 0 away from any optical QSO position in LBQS
field 1140+0000. This plate is in a region of typical NH and has average RASS exposure.
We have selected as a detection criterion that C src – 4
q
C s
bkg , where C src and C s
bkg are the
number of source and background counts in the source aperture. Since only 3 positions in
the control sample were `detected' by this criteria, we estimate a spurious detection rate
of less than 5%. Our criterion corresponds approximately to R src – 2:3oe src , where R src
and oe src are the source count rate and its error, respectively. Such a detection threshold
is justified in studies such as this, where X­ray emitting objects are known from optical
selection to exist at these positions a priori.
Of the 908 QSOs in the LBQS/RASS sample, 92 are detected in X­rays by our criteria.
For the non­detections, we assign an upper limit of 4
q
C s
bkg to the raw counts. For 2
close QSOs (0048+0029 and 0048+0025) we use their (single) detection as an upper limit,
but exclude them in the stacking procedure described in x A.2.. X­ray broadband fluxes
are derived for each QSO from RASS counts and galactic hydrogen column density (NH )
using standard counts­to­flux conversion factors (ROSAT Technical Appendix 1991), an
assumed photon index, and NH values interpolated from Stark et al. (1992). NH values in
the LBQS/RASS range from 1.3 to 5:6 \Theta 10 20 cm \Gamma2 , with a mean of 2.74, yielding typical
conversion factors near 2 \Theta 10 \Gamma11 cts \Gamma1 erg cm \Gamma2 . We use a mean ROSAT (0.1 -- 2.4 keV)
photon index of \Gamma = 2:7 for known radio­quiet (RQ) QSOs, and \Gamma = 2:1 for known
radio­loud (RL) QSOs. These classes are defined below in x 5. For QSOs with no radio data,
we use \Gamma = 2:5. All these values are as derived by Schartel et al. (1995) using the same
LBQS/RASS samples and data. We note that in one common notation (e.g. Wilkes et al.
1994), the X­ray spectral energy index ff is defined by f š / š \Gammaff (so that ff = \Gamma \Gamma 1). About
10% of the objects with no radio data may be radio­loud quasars. For these, the assumption
of \Gamma = 2:5 differs significantly from the correct mean photon index, but the resulting flux
discrepancies have an entirely negligible effect on the results presented here. We calculate
monochromatic X­ray luminosities log l x (and corresponding upper limits) at 2 keV in the
rest­frame, using the photon indices described above. The combined uncertainty in the
flux of an individual QSO due to NH interpolation, uncertainty in \Gamma, and counts­to­flux
conversion calibrations is Ÿ 30%.
As expected, the mean redshift of the 92 detected QSOs is significantly lower than for
non­detections (0.74 vs. 1.36), and their mean B J are brighter (17.8 vs. 18.3, see Figure 1a
& b). The fraction of QSOs detected as a function of NH is ú 10% for NH Ÿ 5 \Theta 10 20
(see Figure 1c). Since only 2% of the LBQS/RASS sample have galactic column densities

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larger than this, and since the NH distributions of detections and non­detections are not
significantly different in two­sample tests, we conclude that Galactic NH does not strongly
affect the detection probability in the LBQS/RASS sample.
Detected objects span a (0.1--2.4 keV) flux range of 0.5 to 5:5 \Theta 10 \Gamma12 with a mean
of 1:1 \Theta 10 \Gamma12 erg cm \Gamma2 s \Gamma1 . The lowest (most sensitive) flux upper limit in the sample is
4.2\Theta10 \Gamma13 erg cm \Gamma2 s \Gamma1 . The peak of the flux histogram is at about 8 \Theta 10 \Gamma13 erg cm \Gamma2 s \Gamma1 ,
and this should approximately correspond to the X­ray flux completeness limit for LBQS
QSOs in the RASS. This limit is a function of the RASS exposure time, which has a bimodal
histogram for the LBQS fields, with two peaks centered near 500 and 650 s (Figure 1d).
Thus the quoted X­ray flux limit, although indicative, is not strictly applicable to all fields
of the LBQS. In any case, the bulk of our analysis is based on stacking (see x A.2. below),
which obviates the distinction between detections and non­detections by summing counts
from all QSOs within chosen groupings or bins.
For the 92 LBQS/RASS detections, Table 1 contains the X­ray and optical data, with
luminosities calculated as described in the text. Data for both detections and non­detections
are available in this format on CD­ROM. Columns in Table 1 are as follows: (1) Name of
the LBQS QSO, (2) Redshift, (3) B J magnitude, (4) Extinction AB , in magnitudes, (5)
Galactic hydrogen column density NH in units 10 20 cm \Gamma2 , (6) RASS source counts C src , (7)
RASS background counts normalized to the source aperture area, C s
bkg , (8) RASS exposure
time T , (9) Logarithm of the X­ray luminosity in erg s \Gamma1 Hz \Gamma1 , (10) Logarithm of the
optical luminosity in units erg s \Gamma1 Hz \Gamma1 , (11) The slope ff ox of a hypothetical power law
connecting 2500 š A and 2 keV, (12) Notes, including class designations. For radio loudness,
we note RL, RQ, or RA, where RA means ambiguous (when a radio flux upper limit is
consistent with either a radio­loud or a radio­quiet designation, see x 5.). QSOs with clear
broad absorption lines (x 6.), are noted as BAL, and strong FeII QSOs (see x 7.) are noted
as Fe.
4. OPTICAL TO X­RAY POWER LAW SLOPES
The best­fit linear regression of log l x vs. log l opt yields an apparent power law
relationship between X­ray and optical luminosities that has been well­studied in the past,
particularly using data from the Einstein satellite (e.g., Zamorani et al. 1981, Tananbaum
et al. 1986, Wilkes et al. 1994). Similar correlations have been demonstrated in other
wavebands (e.g., Kriss 1988, Green, Anderson, & Ward 1992). Brinkmann et al. (1994)
have performed a ROSAT study of a heterogeneous sample of cataloged QSOs detected
in both the RASS and the Molonglo Reference Catalog of radio sources (Large et al.

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1991). The current study is the first analysis of the optical to X­ray properties of a large,
optically­selected sample using data from the ROSAT satellite.
The slope of a hypothetical power law connecting 2500 š A and 2 keV is defined as
ff ox = 0:384 log l opt
l x
), so that ff ox is larger for objects with stronger optical emission relative
to X­ray. Figure 2a shows the ff ox histogram for the LBQS/RASS sample, which we
contrast to two very different samples of X­ray­observed QSOs. The open histograms depict
the entire sample including non­detections, which are lower limits to ff ox . Shaded regions
represent detections only. All samples have been restricted to log l opt ? 29:5 for comparison
to the LBQS. We thus cull 345 QSOs from the Einstein Observatory Extended Medium
Sensitivity Survey (EMSS) sample (Figure 2c, Stocke et al. 1991), a substantially complete
X­ray­selected sample starting from optically­identified, serendipitous X­ray sources in
Einstein pointed IPC observations. We include 460 QSOs from the sample of Wilkes et al.
(1994), a heterogeneous compilation of optically and radio­selected QSOs that were targets
of Einstein IPC pointings (Figure 2b). Exposure times of pointed observations are typically
longer than RASS exposures by factors of 4 to 60. Thus, about 60% of the Wilkes et al.
sample is detected, and flux sensitivities range as low as ú 1 \Theta 10 \Gamma14 erg cm \Gamma2 s \Gamma1 .
The probability that the LBQS/RASS distribution of ff ox is drawn from the same
parent population as those of either the EMSS or Wilkes et al. samples is less than 0.01%,
as determined by a Kaplan­Meier two­sample test that incorporates limits (Feigelson &
Nelson 1985). However, the same test shows that the EMSS and Wilkes et al. distributions
of ff ox are consistent with each other. The survivor functions (the Kaplan­Meier estimate of
the cumulative number of objects with ff ox greater than a given value) for the three samples
are contrasted in Figure 2d. The ff ox histograms for the two comparison samples extend to
values near 2.0, including objects with very weak X­ray emission not detected in the RASS.
Figure 3 shows log l opt vs. log l x for the LBQS/RASS sample. To study only detections
excludes information from 90% of the LBQS/RASS QSOs, comprising nearly half the
total X­ray source counts from the ensemble of 908 LBQS/QSOs. On the other hand, (as
discussed in the x A.1.), the large fraction of upper limits to l x renders the survival analysis
(ASURV) regressions unreliable. By stacking the X­ray data (discussed in detail in x A.2.),
we effectively increase the sensitivity of the X­ray observations, and include information
from all QSOs regardless of detections status. For instance, only one individual QSO is
detected with ff ox ú 1:7, whereas stacking allows us to study some properties of an average
QSO with this continuum energy slope. Figure 4 shows the result of stacking LBQS QSOs
in 5 bins each of galactic column density NH and optical luminosity log l opt . All but 2 of
the 25 bins are detections by our criteria, illustrating the power of the stacking technique.
We use GaussFit (Jefferys et al. 1988a,b) for weighted orthogonal regression (hereafter,

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WOR) of the stacked points (see x A.3.), and find a relationship between X­ray and optical
luminosity (Figure 4a) such that
log l x = 0:86(\Sigma0:06) log l opt + 0:3(\Sigma1:9):
This non­unitary slope is highlighted by a correlation of ff ox with log luminosity, seen
in Figure 4(b) for optical, and Figure 4(c) for X­ray luminosity. The best fit WOR for ff ox
with optical luminosity yields
ff ox = 0:08(\Sigma0:02) log l opt \Gamma 0:9(\Sigma0:7):
To examine the effect of our choice of bins on these results, we compare WOR fits to
ff ox (l opt ) using several very different binnings in Table 2. Most fit results are consistent
within ! 1:5oe. A variety of reasonable spectral assumptions for ff o and \Gamma all lead to
non­linear slopes for the log l x (log l opt ) relation. Boyle et al. (1993) derived a nearly
identical slope (0:88 \Sigma 0:08) for the log l x (log l opt ) relation from a sample combining 42
QSOs X­ray­selected in deep ROSAT exposures with the EMSS sample. Similar slopes
have been published in many earlier studies (e.g., Wilkes et al. 1994) using survival analysis
on the fluxes of optically selected QSOs that were also Einstein targets. Margon et al.
(1992) stacked the X­ray images of 146 LBQS QSOs serendipitously observed by Einstein.
We note that for the binning in Table 2 most similar to that of Margon et al. (1992), we
derive the identical slope and intercept.
Figure 4(d) demonstrates that ff ox also correlates with redshift, with a similar slope.
Using bivariate Spearman rank tests (as implemented in ASURV; see x A.1.) on stacked
points, we find that correlations of ff ox with either of log l opt or redshift are significant
at ? 99:7% confidence for these data. Partial Spearman Rank Analysis (hereafter PSRA;
Kendall & Stuart 1976) allows for the more general multivariate case, using a matrix
of bivariate Spearman rank statistics as input. PSRA tests for correlations between
subsamples of the matrix parameters while holding constant all other variables in the
matrix. We find that the strength of correlations between any pair of ff ox and log l opt ,
log l x , and redshift are significant at ? 99:5%. This result is not surprising: since the
majority of QSOs in the magnitude­limited LBQS sample have apparent magnitudes near
the plate limit, a strong correlation between redshift and optical luminosity exists. Thus, we
cannot determine whether ff ox depends more strongly on luminosity or redshift. However,
using different samples, Avni & Tananbaum (1986), Wilkes et al. (1994), and others have
found that ff ox depends primarily on log l opt . Most of our discussion will thus focus on this
latter dependence.

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The observed slope of an ff ox (log l opt ) relation may depend on a number of factors:
1) both the intrinsic and assumed spectral slopes in the optical and X­ray regimes, 2) the
luminosity function and evolution in each of these bandpasses, and 3) a variety of selection
effects and biases. The last point has been highlighted recently by Franceschini et al.
(1994), who find slopes of the l x ( l opt ) relation consistent with linearity using an X­ray
bright subset of the EMSS (Maccacaro et al. 1991) plus the deep ROSAT survey of Boyle
et al. (1993).
An important final check on our stacking technique is to run exactly these same tests
on our control sample. We have appended the X­ray control data to the actual LBQS
optical data used above. The results, using the same bins, are shown in Figure 5. All
points are limits, except for a single detection that is barely realized (at 4.08
q
C s
bkg ) in
one of the 25 bins. The only significant correlation, between log l opt and upper limits to
log l x (Figure 5a), is expected since these luminosities have been multiplied by the identical
redshift factor.
5. RADIO­QUIET vs. RADIO LOUD
Optically­selected samples of QSOs appear to be separated into two distinct
populations, radio­loud (RL) and radio­quiet (RQ; e.g., Kellerman et al. 1989). It is now
accepted that for a given optical luminosity, the average X­ray luminosity of RL QSOs
is higher than that of RQ QSOs (e.g., Zamorani et al. 1981, Avni & Tananbaum 1986,
Worrall et al. 1987). Furthermore, power law fits to the X­ray spectrum of RL QSOs are
characterized by flatter slopes (e.g., Wilkes & Elvis 1987, Lawson et al. 1992, Shastri et al.
1993). The ROSAT X­ray properties of radio­loud QSOs have been studied by Brinkmann
et al. (1994) and Brunner et al. (1992) using the Molonglo (Large et al. 1991) and K¨uhr et
al. (1979) surveys, respectively.
The radio properties of LBQS QSOs have been investigated using VLA observations at
8.4 GHz sensitive to about 0.25 mJy (the 3oe noise limit; Visnovsky et al. 1992, Hooper et
al. 1995). This VLA sample was selected to cover the brightest ú 1=4 of the QSOs over
the full redshift range of the LBQS. We also include 26 (much less sensitive) detections
from the 5 GHz sky surveys of (Condon et al. 1989) or 408 MHz (Large et al. 1981). In
sum, radio data are currently available for 237 QSOs that also have high quality RASS
data. We convert all radio fluxes to 8.4 GHz by assuming a radio spectral slope of \Gamma0:5:
For purposes of comparison, we define an object as radio­loud if the log ratio of the emitted
monochromatic luminosities at 8.4 GHz and 4410 š A , log R j log (l 8:4 GHz =l
4410 š A
), is greater
than unity. In the current sample, this ratio ranges from (an upper limit of) \Gamma0:70 to 4.54,

-- 12 --
with a mean of \Gamma0:06 from survival analysis. A different definition of radio loudness, which
divides QSOs into two populations at an 8.4 GHz radio luminosity of about 10 25 W Hz \Gamma1 ,
would redefine 2 more QSOs as radio­loud, and does not substantially affect any of the
results we present here.
Included in our QSO subsamples defined by radio loudness are only those QSOs with
radio detections or limits that categorize them unambiguously as RL or RQ QSOs. There
is only 1 RL QSO below z = 0:4, compared with 20 RQ QSOs. Furthermore, z = 0:4
corresponds to the mean redshift of QSOs with MB = \Gamma24: Hooper et al. (1995) and
Della Ceca et al. (1994) find that the fraction of RL QSOs decreases abruptly for absolute
magnitudes fainter than this. There is also only 1 RL QSO above z = 2:4, compared to 26
RQ QSOs. For these reasons, to enable a fair comparison between the RL and RQ QSO
samples, we restrict the redshift range of both samples to 0:4 ! z ! 2:4. This leaves 40 RL
QSOs (z = 1:2 \Sigma 0:5), and 147 RQ QSOs (z = 1:4 \Sigma 0:6).
Of RQ QSOs, 16 (11%) are detected in the RASS, compared to 10 RL QSOs (25%).
We can compare count rates in RL and RQ QSO samples independent of assumed spectral
models or detection thresholds via stacking. For convenient comparison, we quote average
RASS count rates normalized to counts (per QSO) using a typical RASS exposure time
of 600 s. The mean number of counts from stacking is 12:9 \Sigma 1:2 sec \Gamma1 for RL QSOs,
significantly higher than the 8.0\Sigma0:6 counts we find for RQ QSOs. Since all the RQ
QSOs are from the somewhat optically brighter VLA­observed subsample (as compared
to less than half the RL QSOs), the intrinsic difference may be even stronger. However,
the observed difference here is nearly compensated for by the difference in mean redshifts
between the RL and RQ subsamples.
As usual, to derive X­ray fluxes and luminosities requires the assumption of an X­ray
spectral slope. Unlike most previous studies, we have mean ROSAT spectral slopes available
from these identical samples and data (Schartel et al. 1995). We thus assign spectral slopes
\Gamma = 2:1 to RL, and \Gamma = 2:7 to RQ QSOs. From stacking all QSOs in the RL and RQ
subsamples, we find overall means (with their dispersions) for log l x of 27:34 \Sigma 0:04 and
27:08 \Sigma 0:03, so that RL QSOs appear to be about twice as luminous in X­rays. For mean
ff ox values, we find 1:46 \Sigma 0:13 for RL and 1:61 \Sigma 0:15 for RQ QSOs. The optical­to­X­ray
properties of these 40 RL and 147 RQ QSOs are compared in Figure 6. We stacked RL
and RQ QSOs separately in bins of redshift (bin edges are 0.4, 0.6, 1, 1.4, 2.4). Although
the number of RL QSOs in these bins is small (3, 11, 14, and 12, respectively), we note
consistently larger ff ox for RQ QSOs. In the highest redshift bin (z ú 1:9), RL QSOs
are significantly more luminous in X­rays, by a factor of about 5. This is in qualitative
agreement with a variety of previous Einstein studies (e.g., Bechtold et al. 1994, Wilkes et

-- 13 --
al. 1994, Worrall et al. 1987, Zamorani et al. 1981).
The trends in luminosity in Figure 6a and 6c suggest that ff ox may be approximately
constant in RL QSOs, i.e., these objects maintain a nearly linear relationship between l opt
and l x . This is quantified by the Gaussfit WOR listed in Table 2 for RL QSOs, which is
consistent with no trend of ff ox with l opt . In RQ QSOs, on the other hand, l x appears
to increase more slowly than l opt , so that ff ox increases with l opt . Since the slope of
the ff ox ( l opt ) relation for RQ QSOs appears to be similar to that of the LBQS/RASS
sample as a whole (see Table 2), the increase in ff ox with luminosity found for the overall
LBQS/RASS sample may be attributable to the contribution of the 9/10 of QSOs that are
radio­quiet. However, it is clear from Table 2 that the formal difference in slope between
RL and RQ subsamples is not significant, probably due to the small number of known
RL QSOs. Wilkes et al. also found the slopes of an assumed ff ox (log l opt ) relation to be
consistent for their RL and RQ subsamples. Based on a very small sample of high redshift
PSPC pointings, Bechtold et al. (1994) and Pickering, Impey, & Foltz (1994) similarly find
evidence for an upward trend in ff ox with luminosity in RQ QSOs, but not in RL QSOs, as
seen in Figure 6b.
The mean ff ox values we find above appears to differ by less than 1oe between RQ and
RL QSOs. This result may be less dramatic than previous work for a variety of reasons: 1)
our conservative use of dispersion rather than the error in the mean (see x A.2. below), 2)
our attempt to match redshift distributions, 3) our use of the correct X­ray spectral slopes
and homogeneous X­ray data. Selection bias in the radio observations might also affect our
result. The most rigorous comparison between RL and RQ QSOs would exclude those (RL)
QSOs found by correlation with the non­VLA surveys. However, their exclusion does not
significantly change our results, and would in any case significantly decrease the RL sample
size. The apparent increase with l opt in the separation of ff ox between RL and RQ QSOs
evident in our Figure 6 warrants further investigation to clarify the strength and cause of
observed trend.
6. BAL vs. non­BAL QSOs
About 10 ­ 15% of optically­selected QSOs have optical/UV spectra that show
deep absorption troughs displaced blueward from the corresponding emission lines in the
high ionization transitions of C IV, Si IV, N V, and O IV. Years after the discovery of
broad absorption line (BAL) QSOs, the geometry, covering factor, temperature, density,
metallicity and ionization parameter of the absorbing clouds are still poorly understood.
Since BAL spectra in the UV are often partly saturated and may contain unresolved

-- 14 --
components, the properties of BAL clouds are not well constrained by optical/UV data
alone. Techniques have recently been developed by Mathur (1994) and Mathur et al. (1994)
that simultaneously exploit UV and X­ray spectra to constrain the allowed ranges of the
parameters just listed. An application of these techniques to BAL QSOs may eventually
provide stronger constraints on BAL clouds, but to date the X­ray properties of BAL
QSOs as a class are only poorly understood, partly for lack of a homogeneous sample with
available X­ray data.
Our BAL QSO subsample includes only those with clear BALs in their optical spectra,
and we conservatively exclude several QSOs with ambiguous BAL classifications, resulting
in a subsample of 37 BAL QSOs (each noted accordingly in Table 1). The broad absorption
lines just blueward of CIV that are minimally required for a BAL QSO classification here
cannot be detected in the optical below z ú 1:3. Therefore, to enable a fair comparison to
our BAL QSO subsample (z = 1:9), we truncate the non­BAL sample below redshift 1.3,
leaving 36 BAL and 363 non­BAL QSOs with high quality RASS data. Once this is done,
no significant differences are seen in the distributions of redshift, B J magnitude, galactic
NH , or RASS exposure time between the BAL and non­BAL samples.
Only one BAL QSO in the LBQS/RASS sample is detected in the RASS, so that
we cannot perform extensive X­ray analysis of this subsample. However, we can again
examine the average X­ray properties of BAL QSOs by stacking, and by comparing BAL
QSO properties with similar stacked non­BAL samples. One such measure is provided
by comparing the number of net stacked counts of BAL and non­BAL QSO subsamples
(normalized to a 600 s exposure). For the stacked 36 BAL QSOs this value is \Gamma0:15 \Sigma 1:1,
compared to 3:2 \Sigma 0:4 for stacking the subsample of all 363 non­BAL QSOs. Our
conservative upper limit of 4
q
C s
bkg to the stacked counts for the 36 BAL QSOs yields the
following limits assuming \Gamma = 2:5: log l x Ÿ 27:2, and ff ox – 1:6, where log l opt = 31:4 for the
subsample. At the 4oe level, the X­ray properties of BAL QSOs are marginally consistent
with those of the ensemble of LBQS/RASS QSOs as displayed in Figure 4. However,
these limits are also fully consistent with the above 2 \Gamma 3oe suggestion that BAL QSOs are
underluminous or strongly absorbed in X­rays. At the very least, these final conservative
limits show that BAL QSOs as a class are definitively not X­ray loud. A more consistent
comparison of log l opt and ff ox values is obtained if the B J magnitudes for BAL QSOs are
corrected for the presence of the absorption lines. The ``BAL K­correction'' (Stocke et al.
1992) for z ú 2 QSOs is 0:15 \Sigma 0:08. Application of this correction to the mean BAL mag
yields results identical to within the errors.
In a second approach using a Monte Carlo simulation, we randomly picked 1000
subsamples of 36 non­BAL QSOs each from the same list of 363 non­BALs, and stacked

-- 15 --
their X­ray data as with the 36 actual BAL QSOs. Only 5 in 1000 trials stacking non­BAL
subsamples achieve lower net count rates than for the BAL QSO subsample (Figure 7).
Since BAL QSOs may be a subgroup of the class of RQ QSOs (Stocke et al. 1992), we
also compared the BAL subsample to the sample of 94 non­BAL QSOs with z ? 1:3 that
are known to be radio­quiet. From this (somewhat brighter B mag) comparison sample,
we never achieved lower count rates in 1000 trials. Both the above approaches suggest (at
2 \Gamma 3oe) that BAL QSOs as a class are underluminous in X­rays compared with non­BAL
QSOs.
Since ROSAT count rates for QSOs at similar redshift depend on more than bolometric
luminosity, we now consider the possible effects of X­ray spectral properties or Galactic
absorption on our result. The mean Galactic NH is about 2:7 \Theta 10 20 cm \Gamma2 for both BAL
and non­BAL samples. If these represent total line­of­sight hydrogen column densities, then
BAL X­ray spectral slopes would need to be unreasonably soft (\Gamma ?? 3) to account for
the difference in observed counts. This leaves strong absorption intrinsic to the BALs as
the most likely culprit, a result not incongruous with the strong UV absorption that leads
to their BAL classification. Further analysis of the absorbers in BAL QSOs would benefit
from the treatment recently applied to the X­ray/UV absorbing outflows in 3C351 and
3C212 (Mathur et al., 1994, Mathur 1994). However, one deterrent to such analysis has
been the dearth of BAL QSOs at typical BAL discovery redshifts with sufficiently strong
X­ray emission to permit X­ray spectral analysis from exposures of reasonable length.
The only BAL QSO detected in X­rays in the LBQS/RASS sample is 2212--1759. Given
its large redshift of 2.21, and our result that BAL QSOs are likely to be X­ray quiet, this
detected BAL seems worthy of further study. However, since we have estimated a spurious
detection rate of Ÿ 5% from the control sample (x 3.), we expect at most 1 or 2 BAL QSOs
to be incorrectly identified as a RASS detection. Examination of the LBQS plates reveal
several other possible sources of X­ray emission. One nearby object is a B J = 14:0 star
about 50 00 SE of the BAL QSO position. Conservatively using V = 14:5 and the observed
RASS flux, we find log f x =f V ! \Gamma0:9, consistent with ratios observed for stars of mid­M
type or later (Stocke et al. 1992). However, our optical spectrum of the object (taken with
the MMT Blue Channel spectrograph on 1994 June 1) shows the star to be of type K2 or
earlier, with no emission lines that might indicate chromospheric activity, thus making the
star an unlikely X­ray source. Another stellar object 32 00 from the QSO is (judging by the
LBQS plate prism spectrum) a late K or M star, but with B J = 18:4 it could not produce
the observed X­ray flux. A (B J ú 19:5) galaxy 47 00 from the BAL QSO is also not likely to
be the RASS source given the f x =f V ratios typical of galaxies. We thus believe the BAL
2212­1759 to be the source of the X­rays we have detected in the RASS, and so a good
candidate for X­ray spectral analysis.

-- 16 --
7. FeII vs. non­FeII
There is some evidence that QSOs with strong FeII emission may have different
X­ray properties than otherwise similar QSOs showing weak or nonexistent FeII. Using a
heterogeneous sample of 18 objects (z = 0:15), Shastri et al. (1993) found that (radio­quiet)
QSOs with strong optical FeII emission show softer (steeper) Einstein spectral slopes. In
a heterogeneous sample of 55 QSOs (z ! 0:5, ú 30% radio loud), Corbin (1993) found a
strong anti­correlation between the optical FeII/Hfi ratio and Einstein X­ray luminosity,
as well as a weaker anti­correlation with EW FeII (all these FeII measures used the iron
complex near –4570). Their results suggest that FeII QSOs may be underluminous in
X­rays. However, the physical significance of these correlations has been challenged on the
grounds of incompleteness, differences in sample sizes, and different techniques used to
measure the strength of the iron complexes (e.g., Boroson & Green 1989, Zheng & O'Brien
1990). We attempt to clarify these issues here with a small but homogeneous sample.
From previous LBQS discovery papers (Morris et al. 1991, and references therein), 22
QSOs were flagged as having strong UV FeII emission. Seven more QSOs from Paper II of
the series (Foltz et al. 1989) were classified as possessing strong FeII but were not flagged
in that paper: 0010+0146, 0020­0300, 2237­0234, 2245­0055, 2249+0234, 2356+0207, and
2358­0246. Although the FeII flag represents a subjective judgment, these QSOs are likely
to be among those with the strongest iron emission in the LBQS sample. Of the total of 29
FeII QSOs, 23 have high quality RASS data (all flagged in Table 1). Of 12 FeII QSOs with
radio data, 9 are radio­quiet. 0103--2753 is a BAL QSO, while 1148--0033 and 0107­0235 are
radio­loud QSOs; the latter only is detected in the RASS.
The redshift range most likely to lead to an FeII classification is 0:4 Ÿ z Ÿ 1:5, due to
the iron feature under [Ne IV]–2423. We thus restrict the redshifts of both the FeII and the
comparison non­FeII sample to within this range. This excludes one FeII QSO, 2249+0234,
with z = 0:29. The mean redshift for the sample of 22 FeII QSOs in the LBQS/RASS is
0:88. The comparison sample of 467 non­FeII QSOs has a mean redshift of 0:96. We find
a mean B J magnitude about 0:4 mag brighter for the FeII sample, but since some of this
small difference is due to the iron emission itself, we do not attempt further restrictions to
more closely match the sample distributions. Of the 22 FeII QSOs, 7 are detected in the
RASS. This represents 3 times the overall detection rate in the non­FeII sample. The mean
ff ox for the FeII sample (1:5 \Sigma 0:1) is not significantly different from that of the non­FeII
QSOs (1:6 \Sigma 0:3). However, use of a continuum optical magnitude with the effects of the
FeII emission removed is probably more consistent, and would further decrease the derived
ff ox for FeII QSOs.

-- 17 --
The mean number of counts from stacking the 22 QSOs in the FeII­strong sample is
thus 14:0 \Sigma 1:7 (again quoting RASS counts normalized to a 600 s exposure). A greater
number of counts is achieved for only 2.2% of 1000 subsamples of 22 QSOs randomly
selected from the non­FeII sample (Figure 8) The mean count rate of these non­FeII
subsamples is 7:8 \Sigma 2:6, nearly a factor of two lower. It thus appears that QSOs with strong
UV FeII emission may be unusually strong X­ray emitters.
We now consider the possible effects of X­ray spectral properties or Galactic absorption
on this result. The mean Galactic absorption N H is virtually identical for the two
subsamples (NH ú 2:7 \Theta 10 20 cm \Gamma2 ). Schartel et al. (1995) find for this same FeII
subsample a photon index \Gamma = 2:8 \Sigma 0:2, which is consistent with the value \Gamma = 2:7 \Sigma 0:1
they derive for the non­FeII subsample. With a line­of­sight hydrogen column density
(NH ú 2:7 \Theta 10 20 cm \Gamma2 ), if differing X­ray spectral slopes are to explain a factor of 2
difference in count rates, we would need to assume values of \Gamma ! 2:2 for the FeII QSOs
and \Gamma ? 3:0 for the non­FeII QSOs. The sense of such a trend is in contradiction to the
results of Shastri et al. (1993) mentioned above, albeit for a very different sample. More
importantly, these spectral indices are 3oe in opposite senses from the values measured for
their respective samples (Schartel et al. 1995). Therefore, we believe that a difference in
X­ray spectral index can be ruled out as the sole cause of the observed difference in X­ray
counts.
According to the models of Krolik & Kallman (1988), the continuum source responsible
for creating rest­frame optical FeII lines comes almost entirely from X­rays above about
1 keV. Data from the small, heterogeneous sample of Shastri et al. (1993) suggested
instead that QSOs with stronger optical FeII had, if anything, softer X­ray spectral slopes.
The rest­frame UV FeII multiplets we study here, according to the model, originate at
lower optical depths where soft X­ray and EUV photons contribute to the heating. Our
finding that LBQS QSOs with strong UV FeII are relatively bright in the ROSAT soft
X­ray bandpass is consistent with this model. On the other hand, Schartel et al. (1995)
find no significant differences in X­ray spectral slopes between the LBQS FeII­strong and
comparison subsamples. Stronger tests of the model would be obtained for QSOs with
both optical and UV FeII measurements available for comparison to X­ray slopes and
luminosities.
8. CONCLUSIONS
We detect 10% of the 908 LBQS QSOs observed in the RASS. The strong correlation
between l opt and l x fits a non­linear power law. This is reflected in a correlation between

-- 18 --
the optical­to­X­ray spectral slope ff ox and the rest­frame 2500 š A luminosity such that
ff ox = 0:08(\Sigma0:02) log l opt \Gamma 0:9(\Sigma0:7): This confirms, using a large, homogeneous sample,
similar results found using independent techniques (e.g., Margon et al. 1992, Wilkes et al.
1994).
We offer the first published comparison of the ROSAT X­ray properties of well­defined
subsamples of RL and RQ QSOs. We stack RASS X­ray counts for RL and RQ QSO
subsamples and find only marginal mean differences in log l x and ff ox for RQ QSOs
compared to RL QSOs. However, differences in X­ray emission appear to increase as a
function of redshift (or optical luminosity). The l x ( l opt ) relation appears to be nearly
linear for RL QSOs, while for RQ QSOs the X­ray luminosity may increase more slowly.
This is equivalent to the statement that the ff ox (log l opt ) relation is steeper for RQ QSOs.
In an optically­selected sample such as this, the oft­observed increase of ff ox with l opt
could thus be attributable mostly to the contribution of the ú90% of the sample that is
radio­quiet. Analysis of the strength and origin of these apparent trends will benefit from a
larger number of radio observations of LBQS QSOs or from deeper X­ray observations.
We use stacking to compare a subsample of 36 BAL QSOs to a comparison sample of
non­BAL QSOs in a similar redshift range. Even though one BAL is detected, the BAL
subsample stacks to a ROSAT count rate of \Gamma0:0003 \Sigma 0:002 s \Gamma1 . Conservative upper limits
to l x and ff ox for the BAL subsample are consistent with the properties of LBQS/RASS
QSOs of similar l opt . However, Monte Carlo tests of random non­BAL subsamples result in
similar count rates ! 1% of the time, suggesting that the BAL class is likely to be X­ray
quiet. We suggest that a very soft intrinsic X­ray spectral slope, combined with Galactic
absorption, is insufficient to account for the low X­ray counts from the BAL QSOs. This
leaves strong absorption intrinsic to the BALs as the most likely culprit.
We contrast a subsample of 22 QSOs showing strong UV FeII emission to a sample of
QSOs in a similar redshift range. The stacked FeII QSO subsample has a ROSAT count
rate twice as high as the mean, which occurs ú 2% of the time in Monte Carlo tests of our
comparison sample. The FeII multiplets we study here may be generated at lower optical
depths where soft X­ray and EUV photons can contribute to the heating.
9. ACKNOWLEDGEMENTS
The ROSAT project is supported by the Bundesministerium f¨ur Forschung and
Technologie (BMFT). We thank our colleagues from the ROSAT group for their support.
This research was supported through NASA Grant NAG5­1623. Support for PJG
was provided by the NSF through grant INT 9201412, and by NASA through Grant

-- 19 --
HF­1032.01­92A awarded by the Space Telescope Science Institute, which is operated by
the Association of Universities for Research in Astronomy, Inc., under NASA contract
NAS5­26555. PJG also wishes to thank the Institute of Astronomy and the MPE for their
kind hospitality. NRS acknowledges a Max Planck Fellowship, and CBF the support of
NSF Grant AST 9320715.

-- 20 --
A. STATISTICAL METHODS
Since only about 10% of LBQS QSOs are detected in X­rays, it is critical to include
the information for QSOs that do not meet the detection criteria. We describe briefly our
use here of two methods: stacking and survival analysis. Our most important results are
derived from stacking of the X­ray counts.
A.1. SURVIVAL ANALYSIS
The widely­distributed survival analysis package ASURV (Rev 1.1, LaValley, Isobe
& Feigelson 1992) implements the methods presented in Feigelson & Nelson (1985) for
univariate problems and Isobe, Feigelson & Nelson (1986) for bivariate problems. When
no upper limits are present, all these tests reduce to the expected results from standard
statistical analyses of distributions: means, two­sample tests, correlations or regressions.
The particular ASURV techniques we use are the same as delineated in Green,
Anderson, & Ward (1992). The Kaplan­Meier nonparametric maximum­likelihood
estimator includes either lower or upper limits to the data. This method works well with
any variable whose censoring distribution is independent of the values themselves. This is
clearly not a description of flux measurements in a flux­limited sample such as the RASS,
wherein all the censored values are found near the sensitivity threshold of the survey. The
effects of non­random censoring are greatly decreased when using flux ratios.
For univariate two­sample comparisons, we require a probability P ! 0:02 to consider
two samples to be `significantly different'. A similar criterion is applied to bivariate
correlation analysis. The two­dimensional Kaplan­Meier test (Schmitt 1985, hereafter
2KM) permits linear regression with limits in either axis.
Although the median of a univariate distribution is always well defined, if the lowest
(highest) point in the data set is an upper (lower) limit, the mean is not, since the
distribution is not normalizable, so that the outlying censored point must be redefined as a
detection. Although redefinition of a single limit as a detection may be acceptable for some
univariate distributions, if only a small fraction of objects are detected, bivariate regressions
may not converge or can yield misleading results, when many limits at bin edges need to
be redefined as detections. The result is that the derived best­fit linear regression may fall
below most points in a plot (e.g., of log l opt vs. log l x , see Figure 3), and is quite sensitive
to the adopted bin sizes. Results from survival analysis may thus depend strongly on the
number of detections, and therefore on the detection threshold, since in a flux­limited

-- 21 --
sample, most detections are near that threshold (e.g., Anderson & Margon 1987). For these
reasons, when raw data are available, our analysis relies strongly on stacking.
A.2. X­RAY FLUX STACKING
Stacking makes unbiased use of the X­ray information from all objects, a feature that
is ideally suited to a large sample with raw source and background counts available. Results
from stacking are independent of the adopted X­ray detection threshold (see Anderson &
Margon 1987). X­ray stacking has proven useful in a variety of astrophysical applications
(e.g., Caillaut & Helfand 1985, Anderson & Margon 1987). Indeed, the technique was
already used on a subsample of 146 LBQS QSOs serendipitously included in Einstein
pointed observations (Margon et al. 1992).
In the current study, we use our raw RASS source counts in an analogous procedure
to find the average X­ray flux for a selected subsample of QSOs. The raw RASS counts
in the source and background apertures for each QSO are separately summed, as are their
effective exposure times. The final, stacked QSO effectively has a much longer ROSAT
exposure time, and thus a much more sensitive X­ray observation. Errors in both source
and background counts are correctly propagated in the stacking process. The detection
threshold for a stacked QSO is defined identically to that for an individual QSO as outlined
above. Bins are defined interactively to achieve detections without undue sacrifice of
resolution in the binning parameters (e.g. l opt , redshift, or NH ). Any results we quote are
robust and have been reproduced with a variety of binnings.
Galactic hydrogen column density NH determines X­ray counts­to­flux conversion
factors (CFs). Therefore, when the number of QSOs in tested samples permits, we stack in
bins of NH so that the use of a mean CF causes no more than ú 20% error in X­ray flux for
QSOs within a bin (and thereby an error in ff ox of less than 0.03). The resulting l x or ff ox
values (whose spread within an l opt bin may be seen e.g., in Figure 4), show no correlation
between NH and either l x or ff ox , as expected since (stacked) counts remain the primary
determinant of l x .
We calculate X­ray fluxes for stacked QSOs assuming an X­ray photon index \Gamma
appropriate to the sample, as derived by (Schartel et al. 1995). Errors for the stacked
X­ray luminosities are derived from the errors in X­ray source counts oe i of individual QSOs.
If we represent the number of counts in a stacked image as S, with error oe S , the X­ray
luminosity is proportional to S, with the constant of proportionality k depending on (the
mean values of) NH and redshift, and on the assumed \Gamma. The uncertainty in the value of

-- 22 --
log l x is independent of k, and may be expressed simply as
oe = 0:5 log
` S + oe S
S \Gamma oe S
'
:
Errors in optical luminosity or in redshift are taken to be the rms dispersion of
these values among QSOs in a bin. Although the error in the mean values may be much
lower, use of the dispersion automatically includes such effects as intrinsic dispersion
in QSO properties, magnitude errors, and errors in galactic extinction estimates. For
any waveband, we calculate the log of the mean flux (rather than the mean of log) for
QSOs in a stacking bin, so that the slope we derive between the 2500 š A and 2 keV is
ff ox
eff = 0:384log ! l opt =l x ?.
While only a modest fraction of the QSOs will be individually detected in X­rays, the
entire RASS­observed sample of 908 QSOs is effectively utilized in these stacked X­ray
fluxes, to obtain (in most cases) X­ray detections of the stacked QSO within each bin.
Binning and stacking thus allows us to study the evolution of X­ray properties, and the
relationship between X­ray and optical continuum luminosities. Novel stacking techniques
have recently been developed that allow objects to be binned together retaining energy
information for X­ray spectral analysis, even through a range of Galactic hydrogen column
densities (Schartel et al. 1995). The spectral slopes derived for a given sample may then be
used on stacked counts for these samples for calculation of mean fluxes and luminosities, as
they are in the current work for the full LBQS/RASS sample, as well as the RL and RQ
QSO subsamples.
A.3. LINEAR REGRESSION
Unless the intrinsic physical relationships underlying correlations between observed
parameters are known, the simplest and least biased estimator of the form of their
interdependence should be used. The simplest relationship is linear, and may be estimated
by ordinary least squares (OLS) regression when all points are detected. The least biased
such line is found by weighted orthogonal regression (WOR), which makes no assumptions
as to which variable is dependent. For stacked QSO data that has no (or an insignificant
number of) limits, we apply weighted orthogonal regression using GaussFit (Jefferys et
al., 1988a, b). GaussFit yields error estimates on the fit, and can incorporate the general
heteroscedastic case, where measurement errors are different for each point and in each
variable.

-- 34 --
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Fig. 1.--- Basic properties of the LBQS/RASS sample. Histograms of the entire LBQS/RASS
sample (open) and the X­ray detections only (shaded). The sample includes 908 QSOs with
RASS data uncontaminated by nearby unrelated sources, and with exposure times – 300 s.
(a) B J magnitudes from the APM direct plates. (b) Redshift. (c) Galactic hydrogen column
density from Stark et al. (1992). (d) Exposure time in the ROSAT All­Sky Survey.
Fig. 2.--- X­ray to optical spectral slope for 3 large QSO samples. Shaded histograms of ff ox
represent X­ray detections, while open histograms depict the entire sample, including non­
detections, which are lower limits to ff ox . All samples have been restricted to log l opt ? 29:5
for comparison to the LBQS sample, shown in (a). Although both the 460 QSO subsample
of Wilkes et al. (1994) in (b) and the Stocke et al. (1991) EMSS subsample of 345 QSOs in
(c), are taken from Einstein IPC pointings, the former is optically­selected, and the latter
X­ray­selected. Survivor functions (P (? ff ox )) for all three samples are contrasted in (d).
The distribution of ff ox values for the 908 QSOs in the LBQS/RASS sample is significantly
different from that of either of the pointed samples, while the EMSS and Wilkes et al.
distributions are consistent with each other.
Fig. 3.--- X­ray vs. optical luminosity for the LBQS/RASS sample. The 92 LBQS detections
are shown as filled circles with their least­squares mean regression fit (upper solid line). Since
90% of the LBQS/RASS QSOs have only X­ray upper limits (open triangles), a fit using only
detections is probably unreliable. The mean ASURV 2KM regression (dotted line) enables
us to include upper limits. However, since only a small fraction of QSOs are detected, the
2KM regression is well below all the points, and is also not reliable. This illustrates the need
for stacking the LBQS/RASS QSO sample.
Fig. 4.--- Continuum luminosities and spectral slopes for stacked QSO samples. Results of
stacking LBQS/RASS QSOs in 5 bins each of galactic column density NH (bin edges are 1.0,
1.75, 2.25, 3.0, 3.25, 6.0\Theta10 20 cm \Gamma2 ) and rest­frame 2500 š A luminosity log l opt (bins edges
are 29, 30, 30.25, 30.5, 31, 32 erg s \Gamma1 Hz \Gamma1 ). All but 2 of the 25 bins are detections by our
criteria. The usual strong correlation of (monochromatic rest­frame 2 keV) X­ray luminosity
with optical luminosity is seen in (a), with slope 0:86 (\Sigma0:06) between the log­luminosities,
using a weighted orthogonal regression. The decrease in X­ray relative to optical emission
with increasing luminosity (or redshift) is illustrated by the trends in ff ox with log l opt (b),
log l x (c), and redshift (d). Error bars represent dispersions.

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Fig. 5.--- Continuum luminosities and spectral slopes for a stacked control sample. To check
our stacking technique, we repeat the same procedure that generated the previous figure,
this time using our control sample. A marginal detection (filled circle) occurs in one of the
25 bins. The apparent correlation between l opt and upper limits to l x in (a) is expected
since both have been multiplied by the identical redshift factor.
Fig. 6.--- Continuum luminosities and spectral slopes for Radio Loud (RL) vs. Radio­Quiet
(RQ) QSOs. The optical­to­X­ray properties of the 41 RL and 193 RQ QSOs are compared
by stacking RL and RQ QSOs separately in bins of redshift (bin edges are 0.4, 0.6, 1, 1.4,
2.4; this excludes only 2 RL QSOs). Although the number of RL QSOs in these bins is
small (3, 11, 14, and 12, respectively), we note significant differences between RL and RQ
QSO samples that appear to become more pronounced as redshift (or optical luminosity)
increases.
Fig. 7.--- Monte Carlo simulations for BAL QSOs. We stacked 1000 random subsamples of
36 QSOs from a list of 363 definite (z ? 1:3) non­BAL QSOs, for comparison to the true
BAL sample of 36 QSOs. Counts are normalized to a RASS exposure time of 600 seconds.
The number of stacked counts for the BAL sample is indicated, with errors (square root of
the area­normalized background counts) shown as dotted lines to either side. Comparison to
the histogram of stacked counts for the 1000 comparison samples reveals that only 5 in 1000
trials generates equal or fewer counts. The sample of 36 stacked BAL QSOs thus appears to
be X­ray quiet.
Fig. 8.--- Monte Carlo simulations for FeII­strong QSOs. We stacked 1000 random
subsamples of 22 QSOs from a list of 474 (0:4 Ÿ z Ÿ 1:5) QSOs showing no strong FeII
emission, for comparison to the true FeII­strong sample of 22 QSOs. Counts are normalized
to a RASS exposure time of 600 seconds. The number of stacked counts for FeII QSOs
is indicated, with errors (square root of the area­normalized background counts) shown as
dotted lines to either side. Since the probability of obtaining this same number of counts or
larger is ! 2%, the sample of 22 stacked FeII QSOs appears to be X­ray bright.